Half-car Active Suspension Research Articles

Finite-Time Based Fault-Tolerant Control for Half-Car Active Suspension System With Cyber-Attacks: A Memory Event-Triggered Approach

Finite-Time Based Fault-Tolerant Control for Half-Car Active Suspension System With Cyber-Attacks: A Memory Event-Triggered Approach

H∞ Differential Game of Nonlinear Half-Car Active Suspension via Off-Policy Reinforcement Learning

This paper investigates a parameter-free H∞ differential game approach for nonlinear active vehicle suspensions. The study accounts for the geometric nonlinearity of the half-car active suspension and the cubic nonlinearity of the damping elements. The nonlinear H∞ control problem is reformulated as a zero-sum game between two players, leading to the establishment of the Hamilton–Jacobi–Isaacs (HJI) equation with a Nash equilibrium solution. To minimize reliance on model parameters during the solution process, an actor–critic framework employing neural networks is utilized to approximate the control policy and value function. An off-policy reinforcement learning method is implemented to iteratively solve the HJI equation. In this approach, the disturbance policy is derived directly from the value function, requiring only a limited amount of driving data to approximate the HJI equation’s solution. The primary innovation of this method lies in its capacity to effectively address system nonlinearities without the need for model parameters, making it particularly advantageous for practical engineering applications. Numerical simulations confirm the method’s effectiveness and applicable range. The off-policy reinforcement learning approach ensures the safety of the design process. For low-frequency road disturbances, the designed H∞ control policy enhances both ride comfort and stability.

Fuzzy-Based Adaptive Optimization of Unknown Discrete-Time Nonlinear Markov Jump Systems With Off-Policy Reinforcement Learning

This article explores a novel adaptive optimal control strategy for a class of sophisticated discrete-time nonlinear Markov jump systems (DTNMJSs) via Takagi–Sugeno fuzzy models and reinforcement learning (RL) techniques. First, the original nonlinear system model is represented by fuzzy approximation, while the relevant optimal control problem is equivalent to designing fuzzy controllers for linear fuzzy systems with Markov jumping parameters. Subsequently, we derive the fuzzy coupled algebraic Riccati equations for the fuzzy-based discrete-time linear Markov jump systems by using Hamiltonian–Bellman methods. Following this, an online fuzzy optimization algorithm for DTNMJSs as well as the associated equivalence proof is given. Then, a fully model-free off-policy fuzzy RL algorithm is derived with proved convergence for the DTNMJSs without using the information of system dynamics and transition probability. Finally, two simulation examples, respectively, related to the single-link robotic arm and the half-car active suspension are given to verify the effectiveness and good performance of the proposed approach.

Event-Triggered Adaptive Asymptotic Tracking Control of Uncertain MIMO Nonlinear Systems With Actuator Faults.

In this article, an adaptive event-triggered fault-tolerant asymptotic tracking control problem guaranteeing prescribed performance is addressed for a class of block-triangular multi-input and multioutput uncertain nonlinear systems with unknown nonlinearities, unknown control directions, and actuator faults. Through a systematic co-design of the adaptive control law and the event-triggered mechanism, including fixed and relative threshold strategies, a control scheme with low structure and calculation complexity is designed to conserve system communication and computation resources. In this design, the output asymptotic tracking is achieved. The Nussbaum gain technique is incorporated to overcome unknown control directions with a new adaptive law, and a type of barrier Lyapunov function is adopted to handle the prescribed performance control problem, which contributes to a novel control law with strong robustness. The robust controller can address the uncertainties and couplings derived from the system structure, actuator faults, and event-triggered rules, without using approximating structures or compensators. Besides, the explosion of complexity is avoided. It is proved that all signals of the closed-loop system remain bounded, and system tracking errors asymptotically approach 0 with the prescribed performance, while the Zeno behavior is prevented. Finally, the effectiveness of the proposed control scheme is evaluated via an application example of the half-car active suspension system.

Adaptive Fuzzy Observer Control for Half-Car Active Suspension Systems with Prescribed Performance and Actuator Fault

In this paper, an adaptive fuzzy observer-based fault-tolerant controller is designed for a half-car active suspension system under the presence of uncertain parameters, unknown masses of passengers, and actuator failures. To improve the control performance, fuzzy logic systems (FLSs) are employed to approximate the unknown functions caused by uncertain dynamics of the suspension system. Then, an adaptive control design is developed to compensate for the effects of a non-ideal actuator. To improve passenger comfort, both vertical and angular motions are guaranteed simultaneously under the predefined boundaries by the prescribed performance function (PPF) method. Besides, the objectives of handling stability and driving safety are also considered to enhance the suspension performance. The system stability is proved according to the Lyapunov theory. Finally, the effectiveness of the developed approach is evaluated by comparative simulation examples on the half-car model. The simulation results show that the proposed control can improve the suspension performance as the RMS acceleration value is decreased by 68.1%.

An MPC-LQR-LPV Controller with Quadratic Stability Conditions for a Nonlinear Half-Car Active Suspension System with Electro-Hydraulic Actuators

The active suspension system of a vehicle manipulated using electro-hydraulic actuators is a challenging nonlinear control problem. In this research work, a novel Linear Parameter Varying (LPV) State-Space (SS) model with a fictional input is proposed to represent a nonlinear half-car active suspension system. Four different scheduling parameters are used to embed the nonlinearities of both the suspension and the electro hydraulic actuators to represent its nonlinear behavior. A recursive least squares (RLS) algorithm is used to predict the future behavior of the scheduling parameters along the prediction horizon. A Model Predictive Control-Linear Quadratic Regulator (MPC-LQR) is implemented as the control strategy and, to ensure stability, Quadratic Stability conditions are imposed as Linear Matrix Inequalities (LMI) constraints. Furthermore, the inclusion of attraction sets to overcome the conservative performance imposed by the Quadratic Stability conditions is included, as well as a terminal set were the switching between the MPC and the LQR controller is made. Simulations results for the half-car active suspension model over a typical road disturbance are tested to show the effectiveness of the proposed MPC-LQR-LPV controller with quadratic stability conditions in terms of comfort and road-holding.

Composite adaptive backstepping controller design and the energy calculation for active suspension system.

The half-car suspension has the coupling of pitch angle and front and rear suspension. Especially when the suspension model has a series of uncertainties, the traditional linear control method is difficult to be applied to the half-car suspension model. At present, there is no systematic method to solve the suspension power. According to the energy storage characteristics of the elastic components of the suspension, the power calculation formula is proposed in this paper. This paper proposes a composite adaptive backstepping control scheme for the half-car active suspension systems. In this method, the correlation information between the output error and the parameter estimation error is used to construct the adaptive law. According to the energy storage characteristics of the elastic components of the suspension, the power calculation formula is introduced. The compound adaptive law and the ordinary adaptive law have good disturbance suppression, both of which can solve the pitching angle problem of the semi-car suspension, but the algorithm of the compound adaptive law is superior in effect. In terms of vehicle comfort, the algorithm of the general adaptive law can achieve stability quickly, but compared with the composite adaptive law, its peak value and jitter are higher, while the algorithm of the composite adaptive law is relatively gentle and has better adaptability to human body. In terms of vehicle handling, both control algorithms can maintain driving safety under road excitation, and the compound adaptive algorithm appears to have more advantages. Compared with the traditional adaptive algorithm, the power consumption of the composite adaptive algorithm is relatively lower than that of the former in the whole process. The simulation results show that the ride comfort, operating stability and safety of the vehicle can be effectively improved by the composite adaptive backstepping controller, and the composite adaptive algorithm is more energy-saving than the conventional adaptive algorithm based on projection operator.

A Bioinspired Dynamics-Based Adaptive Fuzzy SMC Method for Half-Car Active Suspension Systems With Input Dead Zones and Saturations

Active suspension systems are widely used in vehicles to improve ride comfort and handling performance. However, existing control strategies may be limited by various factors, including insufficient consideration of different operation conditions, such as changing in vehicle mass, defects in strategy design leading to incapability for guaranteeing finite-time stability, lack of considering input effects of dead zone and saturation, excessive energy cost, etc. Importantly, very few results considered the energy-saving performance of active suspension systems although a well-perceived issue in practice. An adaptive fuzzy SMC method based on a bioinspired reference model is established in this article, which is to purposely address these problems and be able to provide finite-time convergence and energy-saving performance simultaneously. The proposed control method effectively utilizes beneficial nonlinear stiffness and nonlinear damping properties that the bioinspired reference model could provide. Therefore, superior vibration suppression performance with less energy consumption and improved ride comfort can all be obtained readily. By using a fuzzy-logic system (FLS), the proposed method is beneficial in compensating for system parameter uncertainties, external disturbances, input dead zones, and saturations. Furthermore, based on the adaptive PD-SMC method, the tracking errors can converge to zeros in finite time. The stability of the equilibrium point of all the states in active suspension systems is theoretically proven by Lyapunov techniques. Finally, simulation results are provided to verify the correctness and effectiveness of the proposed control scheme.

Extended disturbance observer based robust sliding mode control for active suspension system

In this paper, the approach of reduced-order extended state observer (RO-ESO) proposed by Zuo and Nayfeh (J Sound Vib 265(2):459–465, 2003) for estimation of un-modeled dynamics and disturbances in the antilock braking system is extended to the half car active suspension system (HCASs). Reduced-order ESO is used to estimate the lumped parametric uncertainties, un-modeled dynamics, and external disturbances affecting the performance of HCASs. Here, the estimation accuracy is further improved by the modification of RO-ESO. Modified and extended disturbance observer (E-DO) is proposed to estimate these lumped disturbances and their derivatives, thus reducing disturbance estimation error. A sliding mode control (SMC) based controller is designed to stabilize the vehicle body’s heave and pitch motion using an active suspension system, resulting in ride comfort improvement with guaranteed suspension space constraint and road holding. The proposed E-DO-based SMC (E-DO-SMC) controller’s effectiveness and robustness is analyzed by MATLAB simulations conducted on two different road excitations. The results obtained are compared with RO-ESO based SMC (RO-ESO-SMC) and passive suspension system.

Control analysis of vehicle ride comfort through integrated control devices on the quarter and half car active suspension systems

This study proposed an integrated chassis control of the quarter car and half car active suspension systems to enhance vehicle ride comfort and road handling performance. The integrated controls of PID-LQR and Fuzzy-PID were designed to maximize driving comfort by keeping the vehicle wheels in contact with the road surface. The PID control which is commonly used in car manufacturing was set as a controller benchmark. Multiple road conditions such as speed bumps of different heights, 0.1 m < h < 0.3 m and widths, 0.3 m < d < 0.5 m were used in the system for analysis. In comparison with PID-LQR, Fuzzy-PID showed the lowest peak amplitude and reached the stability state in a minimum time against the controller benchmark. This indicates that vehicle ride comfort and road handling performance can be optimized using the proposed Fuzzy-PID control.

Sampled-Data Asynchronous Fuzzy Output Feedback Control for Active Suspension Systems in Restricted Frequency Domain

This paper proposes a novel sampled-data asynchronous fuzzy output feedback control approach for active suspension systems in restricted frequency domain. In order to better investigate uncertain suspension dynamics, the sampled-data Takagi-Sugeno (T-S) fuzzy half-car active suspension (HCAS) system is considered, which is further modelled as a continuous system with an input delay. Firstly, considering that the fuzzy system and the fuzzy controller cannot share the identical premises due to the existence of input delay, a reconstructed method is employed to synchronize the time scales of membership functions between the fuzzy controller and the fuzzy system. Secondly, since external disturbances often belong to a restricted frequency range, a finite frequency control criterion is presented for control synthesis to reduce conservatism. Thirdly, given a full information of state variables is hardly available in practical suspension systems, a two-stage method is proposed to calculate the static output feedback control gains. Moreover, an iterative algorithm is proposed to compute the optimum solution. Finally, numerical simulations verify the effectiveness of the proposed controllers.

Optimized Fast Terminal Sliding Mode Control for a Half-Car Active Suspension Systems

This paper presents an optimized sliding mode controller (OPSMC) for vibration control of active suspension systems. The proposed controller consists of two parts: the first is the fast terminal sliding mode controller which performs fast convergence, and the second is the particle swarm optimization algorithm which is used to achieve the optimal controller’s’ parameters. The merit of OPSMC has quite simple structure and easy to be regulated, as well as improve the tracking performance. The half-car active suspension systems with non-linearity such as the parameters variation and external disturbance are simultaneously taken into account to provide a realistic framework. The control objective is to deal with the classical conflict between minimizing vertical and angular chassis accelerations to increase the ride comfort. Versus, to keep minimum dynamic wheel loads and suspension deflections to ensure the ride safety. Finally, to show the performance of the proposed OPSMC, the comparison with a recently developed efficient method called optimization and static output-feedback control (OPSOFC) is conducted with different roads disturbances.

Static-Output-Feedback Based Robust Fuzzy Wheelbase Preview Control for Uncertain Active Suspensions With Time Delay and Finite Frequency Constraint

This paper proposes a static-output-feedback based robust fuzzy wheelbase preview control algorithm for uncertain active suspensions with time delay and finite frequency constraint. Firstly, a Takagi-Sugeno (T-S) fuzzy augmented model is established to formulate the half-car active suspension system with consideration of time delay, sprung mass variation and wheelbase preview information. Secondly, in view of the resonation between human's organs and vertical vibrations in the frequency range of 4-8 Hz, a finite frequency control criterion in terms of $H_{\infty}$ norm is developed to improve ride comfort. Meanwhile, other mechanical constraints are also considered and satisfied via generalized $H_{2}$ norm. Thirdly, in order to maintain the feasibility of the controller despite of some state variables are not online-measured, a two stage approach is adopted to derive a static output feedback controller. Finally, numerical simulation results illustrate the excellent performance of the proposed controller.

Nonlinear extended state observer-based output feedback stabilization control for uncertain nonlinear half-car active suspension systems

This paper proposes a nonlinear extended state observer-based output feedback stabilization controller for a half-car active suspension system, to overcome factors leading to performance deterioration, such as nonlinearities, parameter uncertainties, unmodeled dynamics, and uncertain external disturbances. Nonlinear extended state observers are first developed to estimate the unmeasurable states and unknown dynamics of heave and pitch motions. Then, finite-time stabilization control laws are synthesized to improve the vehicle body attitude and ride comfort. The proposed control scheme is an improvement over the existing linear extended state observer-based techniques, given its high observation quality and finite-time convergence. From the perspective of practical implementation, the controller is independent of an accurate mathematical model and only requires the measurable output signals. By constructing weighted error and auxiliary state systems, and employing geometric homogeneity theory, the finite-time stability of estimation errors and suspension states is systematically proven within the Lyapunov framework. Furthermore, the zero dynamics stability is analyzed to guarantee the suspension space constraint and road holding. Finally, numerical simulations are conducted on some representative road excitations and the results are compared to the existing solution and passive suspension. The analysis has confirmed the effectiveness and robustness of the proposed control method.

Adaptive Sliding Mode Control for Uncertain Active Suspension Systems With Prescribed Performance

In this article, the adaptive sliding mode (ASM) control scheme of half-car active suspension systems with prescribed performance is studied. Because of the affected by model uncertainty, time-varying parameter, pavement roughness excitation, etc., the study of suspension systems can be regarded as the multivariable nonlinear control problem. First of all, the prescribed performance function (PPF) is applied to constrain the displacement and pitch angle of the suspension systems to ensure the transient and steady-state suspension responses. Second, an integral terminal sliding mode control method with strong robustness is put forward, which can make the system converge rapidly in a finite-time when it is far from the equilibrium point, solve the singularity problem in the control process, and reduce the chattering phenomenon in the traditional sliding mode control. Then, the neural networks (NNs) approximation characteristics are used to deal with unknown items in the design of the controller, and the Lyapunov stability theory is employed to analyze the stability of the closed-loop system. In the end, the comparative simulation results demonstrate the feasibility and effectiveness of the proposed control scheme.

HIZ TÜMSEĞİ PROFİLLERİ İÇİN YARIM TAŞIT MODELİ YAKLAŞIMI KULLANILARAK AKTİF SÜSPANSİYON SİSTEMİNİN MODELLENMESİ VE SİMÜLASYONU

Driving comfort and safety are important research areas in engineering and have been the subject of many studies. The objective of this work is the modeling and simulation of the disruptive effects coming from the road for the car suspension system. Disruptive effects from the road are modeled as bump geometry which represents the speed trap. There are different vehicle models are used in suspension control systems. The half-car model is selected in this study which has four degrees of freedom; the vertical movements of the front and rear axle, pitch and vertical motions of the vehicle body. The suspension system is the most important part of the vehicle that increases driving safety and passenger comfort by reducing road effects. The actively controlled suspension system is a type of vibration suspension structure popular in both the academic research and industrial application. As the control design, Linear Quadratic Regulator (LQR) controller is designed for half car active suspension system. In order to demonstrate the performance of the designed controller, a comparison has been made for the active and passive states for the suspension system. The designed controller was implemented to the active suspension control of the vehicle model modeled in Matlab-Simulink environment. Bump type speed trap profile is modeled as an input of the system. Simulation results show that the disruptive effects from the road is effectively damped when the active suspension is activated.

A novel adaptive actuator failure compensation scheme based on multi-design integration for half-car active suspension system

A new actuator failure compensation scheme in the presence of actuator failures with multi-uncertainties is proposed for half-car active suspension systems based on multi-design integration. A parameterized function has been introduced to denote the multiple failures occurred in the front and rear actuators. An effective feedback controller is designed to obtain asymptotic tracking and closed-loop system stability by employing backstepping technique. Based on the desired controller, multiple adaptive control signals are designed corresponding to each possible failure case. By introducing failure indicator functions and integrating these control signals, a composite controller is constructed to handle all failure patterns, which ensures both pitch and vertical motions of car body to stabilize and track the desired signals. Finally, simulation is conducted to verify the effectiveness of the controller proposed in this study.

Model-free Adaptive Fuzzy Logic Control for a Half-car Active Suspension System

Model-free Adaptive Fuzzy Logic Control for a Half-car Active Suspension System

Adaptive Vehicle Stability Control of Half-Car Active Suspension Systems With Partial Performance Constraints

A novel adaptive controller for the half-car active suspension systems (ASSs), which can improve the riding comfortability and handling stability of the driver, is proposed in this paper. By using nonlinear mapping, it is demonstrated that the nonlinear ASSs with partial performance constraints are transformed into the novel pure-feedback systems without constraints. By introducing a modified dynamic surface control (DSC) into the Lyapunov function, the adaptive neural network (NN) controller is discussed. The unknown continuous functions are estimated by the NNs, and the boundedness of all signals in the closed-loop systems is guaranteed by the Lyapunov stability theory. Meanwhile, the performance constraints are not violated. Finally, the simulations are performed to clarify and verify the effectiveness of the proposed scheme.

CONDITIONS FOR COMPLETE FEEDBACK LINEARISATION ON ACTIVE SUSPENSION SYSTEMS FOR MINING TRUCKS

Abstract This paper presents the design and implementation of a mining truck half-car active vehicle suspension system with a pre-disturbance detection algorithm that aims at reducing driver experienced vibrations. It addresses the complexities and limitations of input output feedback linearisation by addressing challenges of hidden state analysis involving jacobian invertibility and zero dynamics analysis on suspension models. The novelty of this paper entails adopting input state linearisation conditions to develop a set of states that result in complete linearisation having no hidden states. Negative state feedback controller is applied to the linearised system and the results demonstrate improved attenuated displacement and smoother accelerations hence cushioning the sprung load. A test bed is developed and integrated with the controller through the use of Matlab, Simulink and DSpace to demonstrate the active suspension system prototype results. Respectively 81.82 % and 97.5 % displacement and acceleration attenuation are achieved by the implemented linear controller.